Question

The number of distinct real roots of the equation sin pi x= x^2-x+5/4

Answer 1

x=11 is the distinct real roots of the equation

Answer 2

Answer:

The number of distinct real roots of the equation $sin\pi x=x^{2} -x+\frac{5}{4}$   is  1

Step-by-step explanation:

Given equation:

$sin\pi x=x^{2} -x+\frac{5}{4}$

$sin\pi x=(x-\frac{1}{2})^{2} +1$

$sin\pi x=1$

$\pi x=sin^{-1} (1)$

$\pi x=\frac{\pi }{2}$

$x=\frac{1}{2}$

As observed,

$sin\pi x=1$  and $x=\frac{1}{2}$

Hence, the equation $sin\pi x=x^{2} -x+\frac{5}{4}$ has only 1 distinct root and that is $x=\frac{1}{2}$